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Leibniz Filters Revisited

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Abstract

Leibniz filters play a prominent role in the theory of protoalgebraic logics. In [3] the problem of the definability of Leibniz filters is considered. Here we study the definability of Leibniz filters with parameters. The main result of the paper says that a protoalgebraic logic S has its strong version weakly algebraizable iff it has its Leibniz filters explicitly definable with parameters.

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References

  1. Czelakowski, J., Protoalgebraic logics, Kluwer, Dordrecht 2001.

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  2. Czelakowski, J., and R. Jansana, ‘Weakly algebraizable logics’, The Journal of Symbolic Logic, 65 (2000), 641–668.

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  3. Font, J. M., and R. Jansana, ‘Leibniz filters and the strong version of a protoalgebraic logic’, Archive for Mathematical Logic, 40 (2001), 437–465.

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  4. Font, J. M., R. Jansana, and D. Pigozzi, ‘Fully adequate Gentzen systems and the deduction theorem’, Reports on Mathematical Logic, 35 (2001), 115–165.

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  5. Gabbay, D., A. Kurucz, F. Wolter, and M. Zakharyashev, Many-dimansional Modal Logics: Theory and Applications, Elsevier 2002, to appear.

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Jansana, R. Leibniz Filters Revisited. Studia Logica 75, 305–317 (2003). https://doi.org/10.1023/B:STUD.0000009562.05301.ce

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  • DOI: https://doi.org/10.1023/B:STUD.0000009562.05301.ce

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